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puteri [66]
2 years ago
8

Find the values of x and y that make these triangles congruent by the HL Theorem.

Mathematics
1 answer:
RideAnS [48]2 years ago
7 0

According to HL theorem if one leg and hypotenuse of one right triangle are equal to one leg and hypotenuse of other right triangle, then the triangles are congruent.

By using this theorem we can set up the system of equations as follows:

x=y+1 ...(1)

2x+3= 3y + 3 ..(2)

By using equation (1) next step is to plug in y+1 for x in equation (2). So,

2 ( y + 1) + 3 = 3y + 3

2y + 2 + 3 = 3y + 3 By using distribution property.

2y + 5 = 3y + 3

2y + 5 - 5 = 3y + 3 - 5 Subtract 5 from each side.

2y = 3y - 2

2y - 3y = -2 Subtract 3y from each sides.

-y = -2

So, y=2

Next step is to plug in y=2 in equation (1) to get the value of x. Hence,

x= 2+1

=3

So, x=3 and y=2 make these triangles congruent.

So, the correct choice is 3. x = 3, y = 2.

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The two gaps of the series are 236 % and 2.41.

The series is 2(32/100) _, _ , 247/100.

We are given that the series is in ascending order.

Let the missing numbers be x and y respectively.

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Hence, we can write,

2.32 < x < y < 2.47

The given options are:-

231 % = 231/100 = 2.31 < 2.32

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0.36 < 2.31

Hence, it is not the answer.

As, 2.36 < 2.41, hence,

x = 2.36 or 236 % and,

y = 2.41

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The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure.
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Answer:

-4

Step-by-step explanation:

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So, we can just start plugging things in and simplifying, so:

| -6 + 3 | - 6 - 1 = | -3 | -7

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3 years ago
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laila [671]

Answer:

<h2>x = -4</h2>

Step-by-step explanation:

<em>Look a the picture</em>.

Draw the horizontal line <em>y = 2</em>.

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Conclusion: f(x) = 2 → x = -4

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